Line Segment Covering of Cells in Arrangements

  • Matias Korman
  • Sheung-Hung Poon
  • Marcel RoeloffzenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9486)


Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set \(L'\) of line segments such that every cell in the arrangement has a line from \(L'\) defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Matias Korman
    • 1
  • Sheung-Hung Poon
    • 2
  • Marcel Roeloffzen
    • 3
    • 4
    Email author
  1. 1.Tohoku UniversitySendaiJapan
  2. 2.School of Computing and InformaticsInstitut Teknologi BruneiBruneiBrunei Darussalam
  3. 3.National Institute of Informatics (NII)TokyoJapan
  4. 4.JST, ERATOKawarabayashi Large Graph ProjectTokyoJapan

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